Free Printable Diagnostic Test in Mathematics

1.

Which of the following best describes the polygon in the figure?

a)

It is a regular concave hexagon.

b)

It is an irregular convex pentagon.

c)

It is an irregular concave hexagon.

d)

It is a regular convex hexagon.

2.

Your classmate told you that the figure shown at the right is a polygon. Fortunately, your teacher has just discussed the lesson in your class. How will you discuss to him that his answer is incorrect?

a)

The figure is not a polygon because there are sides in the figure that are collinear.

b)

The figure is not a polygon because the sides are not connected.

c)

The figure is not a polygon because it is a solid figure.

d)

All of the above.

3.

Harry is working on his floor plan design for his dream house. He needs to determine the total interior angles of a convex polygon that he wants to use for his flooring. If Harry’s polygon has 6 sides, what is the total sum of its interior angles?

a)

540°

b)

720°

c)

900°

d)

1260°

4.

An irregular polygon with four sides has different angle measurements. Its three angles measure 65°, 100°, and 125°. Therefore, the measure of the fourth angle is 70°. Is the statement true?

a)

Yes, because the sum of an interior angle of a triangle is 360°.

b)

Yes, because the sum of an interior angle of a quadrilateral is 360°.

c)

Yes, because the sum of an exterior angle of a pentagon is 360°.

d)

Yes, because the sum of an exterior angle of a hexagon is 360°.

5.

What is 0.45 as a fraction in lowest term?

a)

9/15

b)

9/20

c)

20/9

d)

15/9

6.

Which of the following is true about the value of 2/3 in decimals?

a)

It is repeating.

b)

It is terminating.

c)

It is both repeating and non-terminating.

d)

It is non-repeating and non-terminating.

7.

On the number line, which of the following square root can be found between the two integers 11 and 12?

a)

√12.5

b)

√130

c)

√174

d)

√164

8.

The diameter of a hydrogen atom is 0.000 000 001 cm. What is its diameter in scientific notation?

a)

$1\times10^{-8}$

b)

$1\times10^{-9}$

c)

$1\times10^9$

d)

$1\times10^9$

9.

In section Sampaguita, 3/5 of the students are boys. 1/3 of the boys wear black socks. What fraction of the class are boys who wear black socks?

a)

1/5

b)

3/8

c)

1/4

d)

1/2

10.

A jar of peanut butter is shaped like a cylinder. It has a radius of 3 dm and a height of 5 dm. How many cubic decimeters of jam does it contain?

a)

$141.3\ dm^3$

b)

$14.13\ dm^3$

c)

$1.413\ dm^3$

d)

$1413.1\ dm^3$

11.

Find the volume of the cylinder whose radius is 4 cm and height is 8 cm. $401.92\ cm^3$

a)

$401.92\ cm^3$

b)

$150.72\ cm^3$

c)

$452.16\ cm^3$

d)

$400.92\ cm^3$

12.

A pyramid has a height of 15 cm. Each side of its base is 5 cm long. What is its volume?

a)

$25\ cm^3$

b)

$30\ cm^3$

c)

$35\ cm^3$

d)

$125\ cm^3$

13.

Which of the following is NOT a set?

a)

collection of whole numbers

b)

collection of days in a week

c)

collection of bright students

d)

collection of colors of the rainbow

14.

Which of the following is an infinite set?

a)

the set of multiples of 5

b)

the set of negative integers

c)

the set of positive integers

d)

the set of even numbers

15.

Which of the following represents set M = {whole numbers between 8 and 12}?

a)

{8, 9, 10, 11}

b)

{8, 9, 10, 11, 12}

c)

{8, 9, 10, 11, 12, ...}

d)

{9, 10, 11}

16.

An empty set or a null set (in symbols, { } or Ø) is a set which does not contain any element. Which of the following best describes an empty set?

a)

The set of numbers divisible by 3.

b)

The set of counting numbers with decimal digits.

c)

The set of whole numbers less than 0.

d)

Both B and C are empty sets.

17.

During the school fair, students were encouraged to join a music club and/or sports club. Among the 50 students, 24 joined the music club only, and 12 joined the sports club only. In the Venn diagram, how many students joined neither music club nor sports club?

a)

4 students

b)

46 students

c)

34 students

d)

10 students

18.

Mr. Lee wants to assess the performance of his Grade 7 mathematics students. He created a form and asked his students to complete it. What method of data collection did he use?

a)

interview

b)

questionnaire

c)

registration

d)

experiment

19.

In statistics, questions that can be answered by collecting data through surveys, interviews, and observations are called statistical questions. These questions have answers that vary from person to person. Which of the following is NOT an example of a statistical question?

a)

What do grade 7 students prefer to eat for lunch?

b)

What is the most favorite K-pop group of female grade 7 students?

c)

How tall are the grade 7 students in Navotas?

d)

What is Carl’s favorite movie?

20.

A supermarket is celebrating its 20th anniversary. The manager has decided to give a gift certificate to every 20th customer who enters. The method of sampling used is _____

a)

Cluster Sampling

b)

Simple Random Sampling

c)

Stratified Random Sampling

d)

Systematic Sampling

21.

The faculty conducted a survey to determine the preferred healthcare service provider of its members. The variable of interest of this study is ___________________.

a)

the most common illness among the faculty members

b)

the number of members in the association

c)

the health care service provider preference of the faculty

d)

the number of members who wish to avail of the health care service.

22.

In the frequency distribution table below, how many students were surveyed?

a)

8 students

b)

24 students

c)

26 students

d)

42 students

23.

Twenty nursing students were given a blood test to determine their blood types, and the results are shown below. Which of the following graphs can best display the data?

a)

bar graph

b)

ogive

c)

line graph

d)

histogram

24.

To accurately allocate a portion on the pie chart with a total 360⁰, percentage of a certain data value must be proportional to the degree of the central angle of the pie. Using the table below, what must be the measure of the central angle of the portion for the fishermen?

a)

90⁰

b)

135⁰

c)

81⁰

d)

54⁰

25.

What must be added to -16 to obtain 32?

a)

16

b)

48

c)

-48

d)

-16

26.

Danica’s account balance in her bank card is ₱5,000. She shopped at the mall and used the card to pay two transactions for ₱1,250 and ₱975. What is her account balance now?

a)

₱2775

b)

₱7225

c)

₱2785

d)

₱721

27.

Hector is standing on a hill 41 meters above sea level. Directly below him, Joseph is working in a tunnel 23 meters below sea level. How far apart are they?

a)

64 meters apart

b)

18 meters apart

c)

943 meters apart

d)

1.782 meters apart

28.

Which of the following expressions is correct?

a)

(20 x 5) + 19 x 6 = 714

b)

(9 + 31) x (7 + 25) = 305

c)

(45÷9) x 7 + 31 = 66

d)

(64–4)÷10 - 3² = 54

29.

Solve the expression: 5⁴ x 2÷ (30÷3) + 45 = _____________

a)

59

b)

184

c)

170

d)

257

30.

Find the value of n that makes the equation correct: −n÷(−2)x 4=8.

a)

1

b)

10

c)

5

d)

4

31.

Thea is asked to simplify the expression x⁸ • x⁵ • x². If you were Thea, how will you simplify it?

a)

Copy the variable x and add the exponents: answer = x¹⁵

b)

Combine the variables and add the exponents: answer = 3x¹⁵

c)

Copy the variable and subtract the exponents: x¹ or simply x

d)

Combine the variables and subtract the exponents: 3x¹ or simply 3x

32.

What is the numerical coefficient of the expression 7x³?

a)

7

b)

x

c)

3

d)

1

33.

Which expression best describes the phrase 'thrice the sum of a number x and five'?

a)

3x + 5

b)

3(x + 5)

c)

3(5) + x

d)

5(x + 3)

34.

The number of terms in an algebraic expression is determined by the number of expressions separated by a plus sign (+) or a minus sign (–). How many terms are there in the expression 3x³ + 2x² + 4x – 9?

a)

1 term

b)

2 terms

c)

3 terms

d)

4 terms

35.

Which is the correct translation for the expression $\frac{x+7}{2}$ ?

a)

twice the sum of a number x and seven

b)

third of the sum of twice a number x and seven

c)

thrice the sum of a number x and seven

d)

half of the sum of a number x and seven

36.

Barry decided to put a fence around his rectangular vegetable garden. If the length of the garden is 5 meters more than twice the width, how long is the fencing materials needed?

a)

2x + 5 meters

b)

6x + 10 meters

c)

2x + 10 meters

d)

2x - 5 meters

37.

What is the product when 2x is multiplied by the trinomial x² – 4x + 3?

a)

2x³ – 8x² + 6x

b)

2x² – 8x + 6

c)

16x

d)

5x² – 5x

38.

Mario is 5 years older than his brother Luigi. If the sum of their ages is 21, how old is Luigi?

a)

8 years old

b)

13 years old

c)

16 years old

d)

5 years old

39.

If 5 less than the number is 19, what is the number?

a)

14

b)

24

c)

9

d)

27

40.

RJ has two pieces of luggage weighing 12.6 kilograms and 9.4 kilograms for his flight going to Palawan. If the airline company gives each passenger a weight limit of 25 kilograms for baggage, how much more can he take on his flight?

a)

at least 3 kilograms

b)

at most 3 kilograms

c)

at least 4 kilograms

d)

at most 4 kilograms

41.

Your classmate was asked to expand (2x – 3)². He answered 4x² – 9. Is his answer correct?

a)

Yes, because squaring a binomial always produces a binomial product.

b)

Yes, because the product rule is correctly applied.

c)

No, because squaring a binomial always produces a trinomial product.

d)

No, because the answer must be 4x raised to 2, added to 9.

42.

A bag contains 5 balls: 2 red (R) and 3 blue (B). In a game of chance, Amara takes a ball out of the bag without looking, notes down the color, and then puts it back into the bag. Amara then takes out another ball, notes down the color and puts it back into the bag.

The table below shows all the possible outcomes for this game.

How many possible outcomes are there?

a)

25

b)

36

c)

10

d)

16

43.

A bag contains 5 balls: 2 red (R) and 3 blue (B). In a game of chance, Amara takes a ball out of the bag without looking, notes down the color, and then puts it back into the bag. Amara then takes out another ball, notes down the color and puts it back into the bag.

The table below shows all the possible outcomes for this game.

What is the probability of drawing blue twice?

a)

9/25

b)

16/25

c)

10/25

d)

2/25

44.

The table below shows the results of outcomes after throwing a pair of dice.

How many possible outcomes of rolling a pair of dice?

a)

6

b)

12

c)

24

d)

36

45.

The table below shows the results of outcomes after throwing a pair of dice.

Which pairs of dice will give the sum of greater than 6 but less than 8?

a)

(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)

b)

(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

c)

(1,5), (2,4), (3,3), (5,1), (4,2), (5,2)

d)

(2,6), (3,5), (4,4), (6,2), (5,3), (3,4)

46.

You are going out in a casual date, how many different outfits can you choose from polo-shirt and T-shirt, Short pants and long pants?

a)

2 possible outfits

b)

4 possible outfits

c)

6 possible outfits

d)

8 possible outfits

47.

A biologist is studying the population of a certain type of bacteria. In one of his samples, the population of bacteria is estimated to be 3.2×10⁷ bacteria. In another sample, taken from a different environment, the population is estimated to be 5.4×10⁶ bacteria.

Express the total population of bacteria from both samples in scientific notation. (Correct answer with a detailed solution will earn 2 points)

4 lines

48.

A biologist is studying the population of a certain type of bacteria. In one of his samples, the population of bacteria is estimated to be 3.2×10⁷ bacteria. In another sample, taken from a different environment, the population is estimated to be 5.4×10⁶ bacteria.

During an experiment, the biologist found that the bacteria population in the first sample increased by a factor of 2.5×10³. Calculate the new population of bacteria in the first sample and express the result in scientific notation.(Correct answer with a detailed solution will earn 2 points)

4 lines

Diagnostic Test in Mathematics

Total questions: 48

Worksheet time: 43mins

Similar Resources on Wayground